Precoding in high-order mimo

ABSTRACT

A high-order Multiple-Input-Multiple-Output (MIMO) transmitter implementing a covariance-based precoding scheme that exploits transmit channel correlation and a method of operation thereof are provided. In one embodiment, covariance-based precoding is performed at the high-order MIMO transmitter based on feedback from a remote high-order MIMO receiver regarding a covariance-based precoding matrix. The covariance-based precoding matrix is, or is derived from, a transmit channel correlation matrix determined by the high-order MIMO receiver for the high-order MIMO transmitter. The covariance-based precoding provides a beam-forming effect when there is a relatively high degree of transmit channel correlation, thereby improving performance of the high-order MIMO transmitter. Further, because changes in the transmit channel correlation occur relatively slowly over time, feedback overhead requirements are substantially reduced as compared to that required for traditional MIMO precoding schemes.

This application claims the benefit of U.S. provisional patentapplication Ser. No. 61/078,279, which was filed Jul. 3, 2008 and thedisclosure of which is hereby incorporated herein by reference in itsentirety.

FIELD OF THE INVENTION

The present invention relates to Multiple-Input-Multiple-Output (MIMO)wireless transceivers, and more particularly relates to a precodingscheme for high-order MIMO transmitters.

BACKGROUND OF THE INVENTION

For Multiple-Input-Multiple-Output (MIMO) wireless communication,multiple antennas are used at both the transmitter and the receiver.Because MIMO increases data throughput without additional bandwidth ortransmit power, MIMO is becoming increasingly popular in wirelesscommunications standards. One issue with MIMO is that transmissionquality degrades in Line-of-Sight (LOS) and poor-scatteringenvironments. More specifically, MIMO relies on an uncorrelated transmitchannel resulting from a multi-path environment. However, in LOS andpoor-scattering environments, transmit channel correlation increases. Asa result, transmission quality decreases.

In order to address this issue, current MIMO transmitters typicallyoperate in a closed-loop configuration. In the closed loopconfiguration, the MIMO transmitter performs transmit channel basedprecoding prior to transmission to a MIMO receiver. One such example ispreceding for MIMO as defined by the Long Term Evolution (LTE) standard.In LTE, the MIMO receiver estimates the transmit channel and selects oneof a number of predefined precoding matrices based on the estimate ofthe transmit channel. The precoding matrices are unitary, and theselected precoding matrix is one which will maximize capacity based onthe estimate of the transmit channel. The MIMO receiver then providesfeedback to the MIMO transmitter, where the feedback includes theselected precoding matrix or a reference to the selected precodingmatrix in a codebook stored by the MIMO transmitter. The MIMOtransmitter then applies the selected precoding matrix to a signal priorto transmission. However, since the transmit channel changes frequentlyand the precoding matrix is selected based on the transmit channel, thetransmit precoding matrix must also be updated frequently. Morespecifically, the MIMO receiver must estimate the transmit channel,select a precoding matrix, and feed back the selected precoding matrixor a reference to the selected precoding matrix to the MIMO transmitterfrequently in order to reflect changes in the transmit channel. UsingMIMO as defined by the LTE standard as an example, a new precodingmatrix is preferably selected and fed back on the order of every 4-5sub-frames.

However, one issue with the transmit channel based precoding scheme ofcurrent closed loop MIMO transmitters is that the transmit channel basedprecoding scheme is not suitable for high-order MIMO. More specifically,as the order (i.e., number of antennas) increases, the complexity of thetransmit channel precoding matrix and therefore the overhead requiredfor feedback of the transmit channel based precoding matrix alsoincreases. As such, there is a need for a precoding scheme forhigh-order MIMO that improves transmission quality and minimizes orsubstantially reduces the overhead required for feedback.

SUMMARY OF THE INVENTION

The present invention provides a covariance-based precoding scheme for ahigh-order Multiple-Input-Multiple-Output (MIMO) transmitter thatexploits long-term transmit channel correlation. In one embodiment,covariance-based precoding is performed at the high-order MIMOtransmitter based on feedback from a remote high-order MIMO receiverregarding a covariance-based precoding matrix. The covariance-basedprecoding matrix is, or is derived from, a transmit channel correlationmatrix determined by the high-order MIMO receiver for the high-orderMIMO transmitter. Further, the feedback regarding the covariance-basedprecoding matrix may be the covariance-based precoding matrix or areference to the covariance-based precoding matrix. The covariance-basedprecoding provides a beam-forming effect when there is a relatively highdegree of transmit channel correlation. Further, because changes in thetransmit channel correlation occur relatively slowly over time, overheadrequired to feed back the information regarding the covariance-basedprecoding matrix from the high-order MIMO receiver to the high-orderMIMO transmitter is substantially reduced as compared to that requiredfor traditional MIMO precoding schemes.

In another embodiment, the high-order MIMO transmitter and thehigh-order MIMO receiver communicate using a modulation scheme, such asOrthogonal Frequency Division Multiplexing (OFDM), such that data issimultaneously transmitted from each transmit antenna on each of anumber of sub-carrier frequencies. In this embodiment, the feedback fromthe high-order MIMO receiver is multiple precoding matrices orreferences to multiple precoding matrices, where each precoding matrixis, or is derived from, a transmit channel correlation matrix determinedby the high-order MIMO receiver for one or more of the sub-carrierfrequencies. Based on the feedback, the high-order MIMO transmitterperforms covariance based precoding for data to be transmitted over eachof the sub-carrier frequencies prior to transmission.

Those skilled in the art will appreciate the scope of the presentinvention and realize additional aspects thereof after reading thefollowing detailed description of the preferred embodiments inassociation with the accompanying drawing figures.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

The accompanying drawing figures incorporated in and forming a part ofthis specification illustrate several aspects of the invention, andtogether with the description serve to explain the principles of theinvention.

FIG. 1 illustrates a pair of high-order Multiple-Input-Multiple-Output(MIMO) devices implementing a covariance-based precoding schemeaccording to one embodiment of the present invention;

FIG. 2 is a block diagram of a high-order MIMO transmitter providingcovariance-based precoding according to one embodiment of the presentinvention; and

FIG. 3 is a block diagram of a high-order MIMO receiver providingfeedback to a high-order MIMO transmitter for covariance-based precodingaccording to one embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The embodiments set forth below represent the necessary information toenable those skilled in the art to practice the invention and illustratethe best mode of practicing the invention. Upon reading the followingdescription in light of the accompanying drawing figures, those skilledin the art will understand the concepts of the invention and willrecognize applications of these concepts not particularly addressedherein. It should be understood that these concepts and applicationsfall within the scope of the disclosure and the accompanying claims.

The present invention provides a covariance-based precoding scheme forhigh-order Multiple-Input-Multiple-Output (MIMO) wireless communicationthat exploits long-term transmit channel correlation. As used herein,high-order MIMO wireless communication uses eight or more transmitantennas and eight or more receive antennas. Note, however, that whilethe present invention is discussed herein with respect to high-orderMIMO, the present invention may be used for lower order MIMO if desired.It should be noted that the benefit of traditional transmit channelbased precoding using fast feedback is outweighed by the cost of thelarge amount of overhead required for feedback needed for high-orderMIMO. Specifically, for a Long Term Evolution (LTE) system, experimentshave shown that for 8×8 MIMO, the precoding gain resulting fromtraditional transmit channel based precoding using fast feedback is only2.5 decibels (dB) as compared to open-loop operation. This amount ofgain does not justify the overhead cost required for fast feedback.However, the covariance-based precoding scheme is preferably a slowfeedback scheme that provides improved performance without the largeoverhead cost needed for fast feedback in traditional transmit channelbased precoding schemes.

FIG. 1 illustrates a pair of high-order MIMO devices 10 and 12(hereinafter MIMO devices 10 and 12) implementing a covariance-basedprecoding scheme according to one embodiment of the present invention.Each of the MIMO devices 10 and 12 may be any type of wireless MIMOcommunication device. For example, each of the MIMO devices 10 and 12may be a base station in a cellular communications network, a mobiledevice having a cellular communication interface such as a mobile smartphone, a broadband access card providing broadband network access to amobile device such as a notebook computer via a cellular communicationsnetwork, an access point or wireless router for a wireless Local AreaNetwork (LAN), a wireless network interface card for accessing awireless LAN, or the like. As an example, the MIMO device 10 may be abase station in a cellular communications network, and the MIMO device12 may be a mobile smart phone.

As illustrated, the MIMO device 10 includes a MIMO transmitter 14, aMIMO receiver 16, and a number of antennas 18-1 through 18-N₁. Note thatin this embodiment, the antennas 18-1 through 18-N₁ are used by both theMIMO transmitter 14 and the MIMO receiver 16. As such, when discussingthe MIMO transmitter 14, the antennas 18-1 through 18-N₁ are referred toherein as transmit antennas 18-1 through 18-N₁. Likewise, whendiscussing the MIMO receiver 16, the antennas 18-1 through 18-N₁ arereferred to herein as receive antennas 18-1 through 18-N₁. The MIMOdevice 12 includes a MIMO transmitter 20, a MIMO receiver 22, and anumber of antennas 24-1 through 24-N₂. Again, in this embodiment, theantennas 24-1 through 24-N₂ are used by both the MIMO transmitter 20 andthe MIMO receiver 22. As such, when discussing the MIMO transmitter 20,the antennas 24-1 through 24-N₂ are referred to herein as transmitantennas 24-1 through 24-N₂. Likewise, when discussing the MIMO receiver22, the antennas 24-1 through 24-N₂ are referred to herein as receiveantennas 24-1 through 24-N₂. The MIMO devices 10 and 12 are preferablyhigh-order MIMO devices. However, the present invention is not limitedthereto.

As discussed below in detail, the MIMO transmitter 14 of the MIMO device10 provides covariance-based precoding based on feedback from the MIMOreceiver 22 of the MIMO device 12. While not specifically discussed, ina similar manner, the MIMO transmitter 20 of the MIMO device 12 mayprovide covariance-based precoding based on feedback from the MIMOreceiver 16 of the MIMO device 10. In one embodiment, a covariance-basedprecoding matrix, or a reference to a covariance-based precoding matrixin a codebook stored by the MIMO transmitter 14, is fed back to the MIMOtransmitter 14 of the MIMO device 10 from the MIMO receiver 22 of theMIMO device 12. The covariance-based precoding matrix is then applied todata symbols prior to transmission in order to provide covariance-basedprecoding. Further, as discussed below in detail, the covariance-basedprecoding matrix is, or is derived from, a transmit channel correlationmatrix for the transmit channel of the MIMO transmitter 14. Sincetransmit channel correlation changes relatively slowly over time, slowfeedback, or long-term feedback, may be used. As used herein, slowfeedback, or long-term feedback, is feedback that occurs substantiallymore slowly than the fast feedback needed for traditional transmitchannel based precoding or over a substantially longer period of timethan the fast feedback needed for traditional transmit channel basedprecoding. For example, the feedback needed for the covariance-basedprecoding may be one-hundred or more times slower than that required fortypical closed-loop MIMO precoding.

When there is low transmit channel correlation (i.e., the transmitchannel correlation matrix is or approaches a random matrix), thecovariance-based precoding matrix used to provide covariance-basedprecoding approaches an identity matrix. As a result, typical MIMOspatial multiplexing gain is exploited. There is typically low transmitchannel correlation when, for example, the MIMO transmitter 14 isoperating in a rich-scattering environment. However, when there is highchannel correlation, the covariance-based precoding matrix exploits thehigh channel correlation to provide a beam-forming effect, therebyimproving the quality of transmission. The high channel correlation mayresult from the large number of antennas of the high-order MIMOtransmitter 14, a Line-of-Sight (LOS) or poor scattering environment, ora combination thereof. Using the covariance-based precoding matrix, theMIMO transmitter 14 naturally and gradually transitions from spatialmultiplexing operation to beam-forming operation as the transmit channelcorrelation increases from a minimum to a maximum, and vice-versa.

FIG. 2 illustrates the MIMO transmitter 14 of the MIMO device 10 of FIG.1 in more detail according to one embodiment of the present invention.This discussion is equally applicable to the MIMO transmitter 20 of theMIMO device 12. In this embodiment, a modulation scheme is utilized inwhich data is simultaneously transmitted from each of the transmitantennas 18-1 through 18-N₁ over a number of sub-carrier frequencies.For example, the modulation scheme may be Orthogonal Frequency DivisionMultiplexing (OFDM), Orthogonal Frequency Division Multiple Access(OFDMA), Single-Carrier Frequency Division Multiple Access (SC-OFDMA),or the like. Note, however, that the present invention is not limitedthereto. The covariance-based precoding scheme discussed herein isequally applicable to a modulation scheme that uses a single carrierfrequency rather than multiple sub-carrier frequencies.

As illustrated, the MIMO transmitter 14 includes a number ofcovariance-based precoders 26-1 through 26-M, where M is the number ofsub-carrier frequencies or sub-bands in the bandwidth of the transmitchannel. The covariance-based precoders 26-1 through 26-M providecovariance-based precoding for data to be transmitted on the sub-carrierfrequencies based on corresponding precoding matrices. In thisembodiment, the precoding matrices are provided to the covariance-basedprecoders 26-1 through 26-M from a feedback reception function 27, whichoperates to receive the feedback from the MIMO receiver 22 of the MIMOdevice 12 (FIG. 1) and, if needed, obtain the covariance-based precodingmatrices based on the feedback. The feedback reception function 27 may,for example, be part of the MIMO receiver 16 of the MIMO device 10. Inone embodiment, the MIMO receiver 22 feeds back either the precodingmatrices or references to the precoding matrices in a codebook or otherdata structure stored by the MIMO transmitter 14. However, otherfeedback types, such as analog sounding, may alternatively be used.Further, in one embodiment, each of the covariance-based precoders 26-1through 26-M uses a separate covariance-based precoding matrix. However,in another embodiment, the same precoding matrix may be used by morethan one of the covariance-based precoders 26-1 through 26-M. Morespecifically, the transmit channel correlation changes relatively slowlyover frequency. As such, the same covariance-based precoding matrix maybe used for more than one contiguous sub-band.

The covariance-based precoder 26-1 operates to apply a L₁×N_(T)covariance-based precoding matrix to a 1×L₁ vector of data symbols for afirst sub-carrier frequency (K₁). For LTE, the data symbols areQuadrature Amplitude Modulation (QAM) symbols. L₁ is the number ofeigen-layers, or simultaneous data streams, that may be transmitted overthe first sub-carrier frequency (K₁). As will be apparent to one ofordinary skill in the art, the number of eigen-layers is determined bythe MIMO receiver 22 based on singular value decomposition (SVD) of atransmit channel matrix estimating the transmit channel for thesub-carrier frequency. The 1×L₁ vector includes one data symbol for eachof the L₁ eigen-layers. N_(T) is the number of transmit antennas 18-1through 18-N₁. In operation, a 1×L₁ vector of data symbols is input tothe covariance-based precoder 26-1. The covariance-based precoder 26-1then applies the L₁×N_(T) precoding matrix for the sub-carrier frequencyto the 1×L₁ vector of data symbols using matrix multiplication toprovide a 1×N_(T) vector of precoded values. The process continues suchthat the covariance-based precoder 26-1 then precodes a next 1×L₁ vectorof data symbols.

In a similar manner, the remaining covariance-based precoders 26-2through 26-M apply corresponding covariance-based matrices to datasymbols for the remaining sub-carrier frequencies (K₂ through K_(M)).Note that each sub-carrier frequency may have a different number ofeigen-layers. As such, the vectors of data symbols input to each of thecovariance-based precoders 26-1 through 26-M may have a different numberof symbols. As a result, the covariance-based precoding matrices appliedby the covariance-based precoders 26-1 through 26-M may also have adifferent number of rows.

After preceding, pilot symbols are inserted, and the output of thecovariance-based precoders 26-1 through 26-M including the insertedpilot symbols are input to virtual antenna functions 28-1 through 28-M,respectively. More specifically, for each of the sub-carrierfrequencies, the number of eigen-layers for that sub-carrier frequencyis typically less than the number of transmit antennas (N_(T)). Forexample, for in 8×8 MIMO, there are typically about five eigen-layersper sub-carrier frequency. In order to utilize all eight antennas eventhough there are less than eight layers for each sub-carrier frequency,the virtual antenna functions 28-1 through 28-M apply a N_(T)×N_(T)constant modulus unitary matrix to the outputs of the covariance-basedprecoders 26-1 through 26-M to provide a virtual antenna effect.

The outputs of the virtual antenna functions 28-1 through 28-M areapplied to an Inverse Fast Fourier Transform (IFFT) function 30, whichperforms per antenna based IFFTs. More specifically, the output of eachof the virtual antenna functions 28-1 through 28-M is a 1×N_(T) vector.In operation, the IFFT function 30 simultaneously performs an IFFT foreach of the transmit antennas 18-1 through 18-N₁. More specifically, theIFFT function 30 performs a first IFFT on first values from the 1×N_(T)vectors output by the virtual antenna functions 28-1 through 28-M, andthe results of the IFFT are provided to the first transmit antenna 18-1.The IFFT function 30 simultaneously performs a second IFFT on secondvalues from the 1×N_(T) vectors output by the virtual antenna functions28-1 through 28-M, and the results of the IFFT are provided to thesecond transmit antenna 18-2. In the same manner, the IFFT function 30simultaneously performs IFFTs for each of the remaining transmitantennas 18-3 through 18-N₁.

FIG. 3 illustrates the MIMO receiver 22 of the MIMO device 12 of FIG. 1in more detail according to one embodiment of the present invention.This discussion is equally applicable to the MIMO receiver 16 of theMIMO device 10. The MIMO receiver 22 includes a Fast Fourier Transform(FFT) function 32 that receives an input from each of the receiveantennas 24-1 through 24-N₂ and performs per antenna FFTs. Morespecifically, the FFT function 32 simultaneously performs an FFT foreach of the receive antennas 24-1 through 24-N₂. The results of the perantenna FFTs are provided to corresponding channel estimation functions34-1 through 34-N_(R), where N_(R) is the number of receive antennas,which in this example is N₂. The channel estimation functions 34-1through 34-N_(R) estimate the transmit channel for each sub-carrierfrequency. The estimates of the transmit channel for each sub-carrierfrequency are provided to a channel correlation determination function36. As discussed below, in this embodiment, the channel correlationdetermination function 36 determines a channel correlation matrix(R_(t)) for each sub-carrier frequency based on the estimates from thechannel estimation functions 34-1 through 34-N_(R).

In one embodiment, the channel correlation matrices (R_(t)) for thesub-carrier frequencies are the corresponding covariance-based precedingmatrices. In another embodiment, when rank is reported back to the MIMOtransmitter 14, for each sub-carrier frequency, columns of a singularvalue decomposition element (V_(t)) of the transmit channel correlationmatrix (R_(t)) corresponding to strong eigen-layers may be used as theprecoding matrix for the sub-carrier frequency. A precoding matrixfeedback function 38 then feeds back the covariance-based precodingmatrices for the sub-carrier frequencies to the MIMO transmitter 14 ofthe MIMO device 10 via the MIMO transmitter 20 of the MIMO device 12.The covariance-based preceding matrices may be fed back by feeding backthe covariance-based precoding matrices themselves, by feeding backreferences or indexes to the covariance-based preceding matrices in acodebook or similar data structure stored by the MIMO transmitter 14, orthe like. As another example, an analog sounding channel may be used tofeed back the precoding matrices to the MIMO transmitter 14.

Returning to the FFT function 32, the results of the per antenna FFTsare also provided to a MIMO decoder 40. The MIMO decoder 40 processesthe outputs of the FFT function 32 to provide a symbol estimate for eachlayer transmitted by the MIMO transmitter 14. A QAM demapper 42 and aForward Error Correction (FEC) decoder 44 then process the symbolestimates from the MIMO decoder 40 to simultaneously recover thetransmitted data for each layer transmitted by the MIMO transmitter 14.The data for each layer is then provided to a data sink. The data sinkmay be, for example, a Media Access Control (MAC) layer of the MIMOdevice 12.

The following is a mathematical description of one embodiment of thepresent invention. This discussion focuses on generating acovariance-based precoding matrix for a sub-carrier frequency. The samemay be done for each sub-carrier frequency or, alternatively, a singlecarrier frequency in a single carrier frequency embodiment. A correlatedMIMO transmit channel (H) can be modeled as

H=H _(w)(R _(t) ^(1/2))′,   (1)

where H_(w) is the spatially white (Rayleigh i.i.d.) MIMO transmitchannel, and R_(t) is the transmit channel correlation matrix for thesub-carrier frequency. The transmit channel correlation matrix (R_(t))is defined as:

$\begin{matrix}{{R_{t} = {E\left\lbrack {\left( {\overset{\rightharpoonup}{h}}_{i}^{row} \right)^{\prime}{\overset{\rightharpoonup}{h}}_{i}^{row}} \right\rbrack}},} & (2)\end{matrix}$

where E is the expected value and {right arrow over (h)}_(t) ^(row) canbe any row of the transmit channel correlation matrix. Further, it canbe verified that:

E[H′H]=E[R _(t) ^(1/2) H′ _(w) H _(w)(R _(t) ^(1/2))′]=R _(t).   (3)

As such, the channel correlation determination function 36 may estimatethe transmit channel correlation matrix (R_(t)) for the sub-carrierfrequency based on the following equation:

$\begin{matrix}{{{\overset{\sim}{R}}_{t} = {\sum\limits_{k}{H_{k}^{\prime}H_{k}}}},} & (4)\end{matrix}$

where {tilde over (R)}_(t) is the estimate of the transmit channelcorrelation matrix (R_(t)) for the sub-carrier frequency and H_(k) isthe estimate of the transmit channel for the sub-carrier frequency forthe kth pilot. Thus, Equation (4) states that the transmit channelcorrelation matrix (R_(t)) can be estimated as the summation of thetransmit channel estimates for the sub-carrier frequency from thechannel estimation functions 34-1 through 34-N_(R) for the kth pilot.The estimated transmit channel correlation matrix, or a referencethereto, may then be fed back to the MIMO transmitter 14 as thecovariance-based precoding matrix for the sub-carrier frequency suchthat the equivalent MIMO transmit channel for that sub-carrier frequencybecomes:

R _(t) ^(1/2) H=H _(w).   (5)

Alternatively, R_(t) ^(1/2), or a reference thereto, may be fed back tothe MIMO transmitter 14.

In another embodiment, when rank is reported to the MIMO transmitter 14,it may be desirable to use columns of a singular value decomposedelement (V_(t)) of the transmit channel correlation matrix (R_(t))corresponding to strong eigen-layers (i.e., large values in D_(t) ^(1/2)of the transmit correlation matrix (R_(t))) as the precoding matrix forthe corresponding sub-carrier frequency. More specifically, the squareroot of the transmit channel correlation matrix (R_(t) ^(1/2)) isdefined by the following equation:

R _(t) ^(1/2) =D _(t) ^(1/2) V′ _(t),   (6)

where V_(t) and D_(t) are the singular value decomposed elements of thetransmit channel correlation matrix (R_(t)). Substituting Equation (6)into Equation (1) provides

H=H _(w) D _(t) ^(1/2) V′ _(t).   (7)

By applying V_(t) to Equation (7), we get the equivalent MIMO channelfor the sub-carrier frequency as

V _(t) H=H _(w) D _(t) ^(1/2).   (8)

When there is low transmit channel correlation, V_(t) approaches anidentity matrix. In contrast, when there is high transmit channelcorrelation, V_(t) approaches beam-forming.

Those skilled in the art will recognize improvements and modificationsto the preferred embodiments of the present invention. All suchimprovements and modifications are considered within the scope of theconcepts disclosed herein and the claims that follow.

1. A method of operating a high-order Multiple-Input-Multiple-Output(MIMO) transmitter, comprising: receiving feedback from a remotehigh-order MIMO receiver regarding a covariance-based precoding matrix,the covariance-based precoding matrix being related to a transmitchannel correlation matrix for the high-order MIMO transmitter thatdefines an existing transmit channel correlation; and precoding aplurality of data symbols based on the covariance-based precoding matrixprior to transmission by the high-order MIMO transmitter.
 2. The methodof claim 1 wherein the feedback is a long-term feedback.
 3. The methodof claim 1 wherein the covariance-based preceding matrix is a transmitchannel correlation matrix for a transmit channel of the high-order MIMOtransmitter.
 4. The method of claim 1 wherein the covariance-basedpreceding matrix is one or more columns of a singular value decomposedelement V_(t) of the transmit channel correlation matrix for a transmitchannel of the high-order MIMO transmitter.
 5. The method of claim 4wherein the one or more columns of the singular value decomposed elementV_(t) are one or more columns of the singular value decomposed elementV_(t) corresponding to values in a square root of a singular decomposedelement D_(t) of the transmit channel correlation matrix for thetransmit channel that are greater than a predetermined threshold.
 6. Themethod of claim 1 wherein precoding the plurality of data symbolscomprises applying the covariance-based precoding matrix to a vectorcomprising the plurality of data symbols.
 7. The method of claim 6wherein the number of data symbols in the vector corresponds to a numberof layers to be transmitted by the high-order MIMO transmitter.
 8. Themethod of claim 1 wherein precoding the plurality of data symbols basedon the covariance-based precoding matrix has a beam-forming effect whena transmit channel of the high-order MIMO transmitter is correlated. 9.The method of claim 1 wherein: receiving feedback comprises receivingfeedback from the remote high-order MIMO receiver regarding a pluralityof covariance-based precoding matrices, each of the plurality ofcovariance-based precoding matrices being for at least one sub-carrierfrequency of a transmit channel of the high-order MIMO transmitter; andprecoding the plurality of data symbols comprises, for each sub-carrierfrequency of the transmit channel of the high-order MIMO transmitter,precoding a plurality of data symbols to be transmitted over thesub-carrier frequency based on a covariance-based precoding matrix fromthe plurality of covariance-based precoding matrices that is for thesub-carrier frequency.
 10. The method of claim 9 wherein precoding theplurality of data symbols to be transmitted over the sub-carrierfrequency comprises performing a matrix multiplication of thecovariance-based precoding matrix for the sub-carrier frequency and avector including the plurality of data symbols to be transmitted overthe sub-carrier frequency.
 11. The method of claim 10 wherein theplurality of data symbols to be transmitted over the sub-carrierfrequency includes one data symbol for each layer to be transmitted overthe sub-carrier frequency.
 12. The method of claim 9 further comprising:for each sub-carrier frequency of the transmit channel, applying aconstant modulus unitary matrix to precoded values resulting fromprecoding the plurality of data symbols to be transmitted over thesub-carry frequency based on the covariance-based precoding matrix forthe sub-carrier frequency to provide a plurality of output values forthe sub-carrier frequency including one value for each transmit antennaof a plurality of transmit antennas of the high-order MIMO transmitter;processing the plurality of output values for each of the sub-carrierfrequencies of the transmit channel to perform a per antenna inverseFourier transform function; and providing results of the per antennainverse Fourier transform function to the plurality of transmit antennasof the high-order MIMO transmitter for transmission.
 13. The method ofclaim 1 wherein receiving the feedback from the remote high-order MIMOreceiver comprises receiving the covariance-based precoding matrix froma feedback function of the remote high-order MIMO receiver.
 14. Themethod of claim 1 wherein receiving the feedback from the remotehigh-order MIMO receiver comprises receiving a reference to thecovariance-based precoding matrix from a feedback function of the remotehigh-order MIMO receiver.
 15. The method of claim 1 wherein receivingthe feedback from the remote high-order MIMO receiver comprisesreceiving the feedback from the remote high-order MIMO receiver via ananalog sounding channel.
 16. The method of claim 1 wherein thehigh-order MIMO transmitter has at least eight transmit antennas and theremote high-order MIMO receiver has at least eight receive antennas. 17.A high-order Multiple-Input-Multiple-Output (MIMO) transmittercomprising: a feedback reception function adapted to receive feedbackfrom a remote high-order MIMO receiver regarding a covariance-basedprecoding matrix, the covariance-based precoding matrix being related toa transmit channel correlation matrix for the high-order MIMOtransmitter that defines an existing transmit channel correlation; andcovariance-based precoding circuitry adapted to precode a plurality ofdata symbols prior to transmission by the high-order MIMO transmitterbased on the covariance-based precoding matrix.
 18. The higher-orderMIMO of claim 17 wherein the feedback is a long-term feedback.
 19. Thehigh-order MIMO transmitter of claim 17 wherein the covariance-basedprecoding matrix is a transmit channel correlation matrix for a transmitchannel of the high-order MIMO transmitter.
 20. The high-order MIMOtransmitter of claim 17 wherein the covariance-based precoding matrix isone or more columns of a singular value decomposed element V_(t) of thetransmit channel correlation matrix for a transmit channel of thehigh-order MIMO transmitter.
 21. The high-order MIMO transmitter ofclaim 20 wherein the one or more columns of the singular valuedecomposed element V_(t) are one or more columns of the singular valuedecomposed element V_(t) corresponding to values in a square root of asingular decomposed element D_(t) of the transmit channel correlationmatrix for the transmit channel that are greater than a predeterminedthreshold.
 22. The high-order MIMO transmitter of claim 17 wherein: thefeedback reception function is adapted to receive feedback from theremote high-order MIMO receiver regarding a plurality ofcovariance-based precoding matrices, each of the plurality ofcovariance-based preceding matrices being for at least one sub-carrierfrequency of a transmit channel of the high-order MIMO transmitter; andfor each sub-carrier frequency of the transmit channel of the high-orderMIMO transmitter, the covariance-based preceding circuitry comprises aprecoder adapted to precode a plurality of data symbols to betransmitted over the sub-carrier frequency based on a covariance-basedprecoding matrix from the plurality of covariance-based precodingmatrices that is for the sub-carrier frequency.
 23. The high-order MIMOtransmitter of claim 22 wherein for each sub-carrier frequency, theprecoder for the sub-carrier frequency is adapted to perform a matrixmultiplication of the covariance-based precoding matrix for thesub-carrier frequency and a vector including the plurality of datasymbols to be transmitted over the sub-carrier frequency.
 24. Thehigh-order MIMO transmitter of claim 23 wherein the plurality of datasymbols to be transmitted over the sub-carrier frequency includes onedata symbol for each layer to be transmitted over the sub-carrierfrequency.
 25. The high-order MIMO transmitter of claim 22 furthercomprising: for each sub-carrier frequency of the transmit channel, avirtual antenna function adapted to apply a constant modulus unitarymatrix to precoded values output from the precoder for the sub-carrierfrequency to provide a plurality of output values for the sub-carrierfrequency including one value for each transmit antenna of a pluralityof transmit antennas of the high-order MIMO transmitter; and an inverseFourier transform function adapted to process the plurality of outputvalues for each of the sub-carrier frequencies of the transmit channelto perform per antenna inverse Fourier transforms, wherein results ofthe per antenna inverse Fourier transforms are provided to the pluralityof transmit antennas of the high-order MIMO transmitter fortransmission.
 26. The high-order MIMO transmitter of claim 17 whereinthe high-order MIMO transmitter has at least eight transmit antennas andthe remote high-order MIMO receiver has at least eight receive antennas.